Why doesn't my plane array align to a curve?
You ran into 3 gotchas.


The transforms on plane and path were not CtrlA applied. The object-level scale was sending deformed planes over the clipping horizon, which I also adjusted. As a general rule, while modeling, scale the mesh in Edit mode, rather than altering the object's transform.
The 'Radius' checkbox was set in the path's curve data tab. This means the scale of the deformed plane-array was responding to the curve's radius, which was somewhere near 100. In Edit Mode, under the Transform panel, I selected all the curve's vertices and set the radius to 1.
(Maybe not one?) The curve was not closed (cyclic). To toggle that, in Edit Mode, hit  AltC 


Here's the file..



(BTW, on BSE, this is the preferred (dedicated) site for exchanging .blend files.)